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Proof step 27 from proof in-payload (previous step)

zbrar[m + n] = mkzentry(key, adr0), zbrar[m] = mkzentry(key0, adr), n = n1 +1, m < # zbrar, m + nused0 < # zbrar, n ≤ nused0 ⊦ key = key0, ∃ n0. n0 < nused0 ∧ zbrar[(m + 1) + n0].entry? ∧ zbrar[(m + 1) + n0].key = key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
zbrar[m + n1 + 1] = mkzentry(key, adr0), zbrar[m] = mkzentry(key0, adr), n1 < nused0, m < # zbrar, m + nused0 < # zbrar ⊦ key = key0, ∃ n0. n0 < nused0 ∧ zbrar[(m + 1) + n0].entry? ∧ zbrar[(m + 1) + n0].key = key

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)